A linear equation can be written as:
[tex]y = a*x + b[/tex]
Where a is the slope and b is the y-intercept.
Defining x as the number of weeks since the start of the year, we can write the linear equations I and B as:
[tex]B(x) =\$70 + \$5*x[/tex]
(initial amount plus the amount that he saves each week times the number of weeks)
Similarly, for Ian we have:
[tex]I(x) = \$30 + \$15*x[/tex]
The graph of these lines can be seen below, where the blue one is I(x) and the green one is B(x).
Now we want to determine how much they had when they had the same amount.
This means that we need to solve:
B(x) = I(x)
Replacing the equations we get:
[tex]\$70 + \$5*x = \$30 + \$15*x[/tex]
Now we can solve this for x:
[tex]\$70 - \$30 = \$15*x - \$5*x[/tex]
[tex]\$40 = \$10*x[/tex]
[tex]\$40/\$10 = x[/tex]
[tex]4 = x[/tex]
So they have the same amount of money in week 4, and each one of them has:
[tex]B(4) = I(4) = \$70 + \$5*4 = \$70 + \$20 = \$90[/tex]
If you want to learn more about this, you can read:
https://brainly.com/question/13075913
